A clutch device includes an outer disk carrier, outer disks, an inner disk carrier, inner disks, and at least one lug. The outer disk carrier has first axially running grooves, a first edge, and a first edge side. Each of the outer disks has radial projections spaced apart by depressions and projecting into the first axially running grooves. The inner disk carrier has second axially running grooves, a second edge, and a second edge side. Each of the inner disks has radial projections spaced apart by depressions and projecting into the second axially running grooves. The lug is arranged between two grooves of the first axially running grooves and extending axially from the first edge side, or arranged between two grooves of the second axially running grooves and extending axially from the second edge side.